LUIS SASTRE SAN EMETERIO

Datos <- read.table("facebook_sample_anon.txt",quote = "\"", comment.char = "")
face <- graph_from_data_frame(d = Datos,directed = FALSE)
plot(face)

##Ejercicio 2 #Para poder conjeturar que nodos son mas importantes en esta red, podemos buscar varios indices de centralidad y asi analizar cuales son dichos nodos. #Divido mi grafo en 20 subgrafos para poder analizarlos mejor y calculo el paremtro degree y el lobby de cada uno:

sg1 <- induced_subgraph(face,1:200)
plot(sg1)

a1 <- round(igraph::degree(sg1,normalized = TRUE),4)
b1 <- lobby(sg1)
max(a1)
## [1] 1
max(b1)
## [1] 21
sg2 <- induced_subgraph(face,200:400)
plot(sg2)

a2 <- round(igraph::degree(sg2,normalized = TRUE),4)
b2 <- lobby(sg2)
max(a2)
## [1] 0.56
max(b2)
## [1] 24
sg3 <- induced_subgraph(face,400:600)
plot(sg3)

a3 <- round(igraph::degree(sg3,normalized = TRUE),4)
b3 <- lobby(sg3)
max(a3)
## [1] 0.265
max(b3)
## [1] 27
sg4 <- induced_subgraph(face,600:800)
plot(sg4)

a4 <- round(igraph::degree(sg4,normalized = TRUE),4)
b4 <- lobby(sg4)
max(a4)
## [1] 0.325
max(b4)
## [1] 28
sg5 <- induced_subgraph(face,800:1000)
plot(sg5)

a5 <- round(igraph::degree(sg5,normalized = TRUE),4)
b5 <- lobby(sg5)
max(a5)
## [1] 0.19
max(b5)
## [1] 18
sg6 <- induced_subgraph(face,1000:1200)
plot(sg6)

a6 <- round(igraph::degree(sg6,normalized = TRUE),4)
b6 <- lobby(sg6)
max(a6)
## [1] 0.22
max(b6)
## [1] 22
sg7 <- induced_subgraph(face,1200:1400)
plot(sg7)

a7 <- round(igraph::degree(sg7,normalized = TRUE),4)
b7 <- lobby(sg7)
max(a7)
## [1] 0.215
max(b7)
## [1] 21
sg8 <- induced_subgraph(face,1400:1600)
plot(sg8)

a8 <- round(igraph::degree(sg8,normalized = TRUE),4)
b8 <- lobby(sg8)
max(a8)
## [1] 0.28
max(b8)
## [1] 31
sg9 <- induced_subgraph(face,1600:1800)
plot(sg9)

a9 <- round(igraph::degree(sg9,normalized = TRUE),4)
b9 <- lobby(sg9)
max(a9)
## [1] 0.385
max(b9)
## [1] 19
sg10 <- induced_subgraph(face,1800:2000)
plot(sg10)

a10 <- round(igraph::degree(sg10,normalized = TRUE),4)
b10 <- lobby(sg10)
max(a10)
## [1] 0.285
max(b10)
## [1] 38
sg11 <- induced_subgraph(face,2000:2200)
plot(sg11)

a11 <- round(igraph::degree(sg11,normalized = TRUE),4)
b11 <- lobby(sg11)
max(a11)
## [1] 0.385
max(b11)
## [1] 40
sg12 <- induced_subgraph(face,2200:2400)
plot(sg12)

a12 <- round(igraph::degree(sg12,normalized = TRUE),4)
b12 <- lobby(sg12)
max(a12)
## [1] 0.415
max(b12)
## [1] 41
sg13 <- induced_subgraph(face,2400:2600)
plot(sg13)

a13 <- round(igraph::degree(sg13,normalized = TRUE),4)
b13 <- lobby(sg13)
max(a13)
## [1] 0.16
max(b13)
## [1] 17
sg14 <- induced_subgraph(face,2600:2800)
plot(sg14)

a14 <- round(igraph::degree(sg14,normalized = TRUE),4)
b14 <- lobby(sg14)
max(a14)
## [1] 0.245
max(b14)
## [1] 29
sg15 <- induced_subgraph(face,2800:3000)
plot(sg15)

a15 <- round(igraph::degree(sg15,normalized = TRUE),4)
b15 <- lobby(sg15)
max(a15)
## [1] 0.195
max(b15)
## [1] 20
sg16 <- induced_subgraph(face,3000:3200)
plot(sg16)

a16 <- round(igraph::degree(sg16,normalized = TRUE),4)
b16 <- lobby(sg16)
max(a16)
## [1] 0.22
max(b16)
## [1] 20
sg17 <- induced_subgraph(face,3200:3400)
plot(sg17)

a17 <- round(igraph::degree(sg17,normalized = TRUE),4)
b17 <- lobby(sg17)
max(a17)
## [1] 0.175
max(b17)
## [1] 17
sg18 <- induced_subgraph(face,3400:3600)
plot(sg18)

a18 <- round(igraph::degree(sg18,normalized = TRUE),4)
b18 <- lobby(sg18)
max(a18)
## [1] 0.2
max(b18)
## [1] 14
sg19 <- induced_subgraph(face,3600:3800)
plot(sg19)

a19 <- round(igraph::degree(sg19,normalized = TRUE),4)
b19 <- lobby(sg19)
max(a19)
## [1] 0.195
max(b19)
## [1] 9
sg20 <- induced_subgraph(face,3800:4039)
plot(sg20)

a20 <- round(igraph::degree(sg20,normalized = TRUE),4)
b20 <- lobby(sg20)
max(a20)
## [1] 0
max(b20)
## [1] 0

#Podemos decir que los diez estudiantes seran los que mayor grado tengan y mayores conexiones tengan en el grafo.

###Ejercicio 3 #(a) El 0.1% de los nodos serian unos 4 nodos que habria que elimimar.

set.seed(1)
rep <- sample(1:4039,4,replace = FALSE)
face1 <- delete_vertices(face,rep)
plot(face1)

cone <- lobby(face1)
mean(cone)
## [1] 32.97571
set.seed(3)
rep1 <- sample(1:4039,4,replace = FALSE)
face2 <- delete_vertices(face,rep1)
plot(face2)

cone1 <- lobby(face2)
mean(cone1)
## [1] 33.03717
set.seed(3)
rep1 <- sample(1:4039,4,replace = FALSE)
face2 <- delete_vertices(face,rep1)
plot(face2)
cone1 <- lobby(face2)
mean(cone1)
## [1] 33.03717

#Asi hasta las mil reproducciones

#(b)